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The incorporation of quantum dots in display technology has fueled a renewed interest in InP-based quantum dots, but difficulty controlling the Zn chemistry during shelling has stymied thick, even ZnSe shell growth. The characteristic uneven, lobed morphology of Zn-based shells is difficult to assess qualitatively and measure through traditional methods. Here, we present a methodological study utilizing quantitative morphological analysis of InP/ZnSe quantum dots to analyze the impact of key shelling parameters on InP core passivation and shell epitaxy. We compare conventional hand-drawn measurements with an open-source semi-automated protocol to showcase the improved precision and speed of this method. Additionally, we find that quantitative morphological assessment can discern morphological trends in morphologies that qualitative methods cannot. In conjunction with ensemble fluorescence measurements, we find that changes to shelling parameters that promote even shell growth often do so at the cost of core homogeneity. These results indicate that the chemistry of passivating the core and promoting shell growth must be balanced carefully to maximize brightness while maintaining emission color-purity.